Question

A glass prism of refractive index $1.5$ is immersed in water $(\mu =4/3)$ as shown in the figure. A light ray incident normally on face $AB$ will get totally reflected from the face $AC$ if

• A. $\theta >{\sin }^{-1}\left(\frac{8}{9}\right)$
• B. $\theta <{\sin }^{-1}\left(\frac{8}{9}\right)$
• C. $\theta ={\sin }^{-1}\left(\frac{8}{9}\right)$
• D. $\theta >{\sin }^{-1}\left(\frac{3}{4}\right)$

Answer 1

The correct option is A $\theta >{\sin }^{-1}\left(\frac{8}{9}\right)$

The light ray is falling normally at the surface $AB$, hence it will pass undeviated.
For getting totally reflected from the surface $AC$, condition of total internal reflection must be satisfied.
$\Rightarrow i>i_c$ ............$\left(i\right)$


From formula,
$i_c={\sin }^{-1}\left(\frac{{\mu }_r}{{\mu }_d}\right)$
$\Rightarrow i_c={\sin }^{-1}\left(\frac{4/3}{1.5}\right)$
$\Rightarrow i_c={\sin }^{-1}\left(\frac{8}{9}\right)$
From $\left(i\right)$,
$i>{\sin }^{-1}\left(\frac{8}{9}\right)$
From geometry, ${90}^{\circ }-i+{90}^{\circ }+\theta ={180}^{\circ }$
$\Rightarrow i=\theta$
Thus, $\theta >{\sin }^{-1}\left(\frac{8}{9}\right)$

Why this question? Tips: Be cautious at the interfaces and apply condition of total internal reflection at the interface as per requirement.